On your behalf, I phonecalled Mike O'Donnell about your shoulder-belt plate. He is the primary author of the 616-page reference book "American Military Belt Plates."
Mr. O'Donnell said you are correct, this version of Great Seal emblem and the nickel-silver plating on the emblem (rather than sliver-plating) strongly indicates it dates from the Indian Wars era into the World War One era. He said this plate's brass body is a manufacturer's "stock" model of plate, meaning the small attachment-slots in its face were positioned to acceptone of several varieties of emblems, according to the customer's desire. He said this particular version of shoulder-belt plate (having the Great Seal emblem) was used mainly by State Militia units, and some Military Schools.
Regards,
Pete [P.C. George]